The present invention relates to the construction of high-speed rotors for the storage of inertial energy and is more particularly directed to an improved spoke arrangement for mounting such a rotor to a central hub.
Today's energy shortages make it increasingly necessary to store energy which becomes available during periods of relatively low energy demand for use during peak demand periods. For example, solar energy is readily available during relatively low-demand daytime periods, but is frequently unavailable during the peak-demand evening hour periods.
It has been suggested to store such excess energy in the form of kinetic or inertial energy utilizing very high-speed flywheels or rotors. One such inertial energy storage rotor is disclosed in U.S. Pat. No. 3,683,216 issued to Richard F. Post, and U.S. Pat. No. 3,741,034 issued to Stephen F. Post. In such systems excess energy, in the form of electrical power, is used to drive an electrical motor-generator to spin the rotor at rates of rotation as high as 20,000 RPM and more. To convert this inertial energy back into usable form, the motor-generator is operated in its generator mode to generate electricity while correspondingly decreasing the rotor's rate of rotation, thereby converting the rotor's inertial energy back into electrical power.
The high speeds at which such rotors have to be spun in order to store useful amounts of energy severely stresses the rotor and associated structural elements such as spokes and requires that they be specially constructed to withstand the centrifugal forces generated by such high rates of rotation.
It is known that the stress to which a rotating ring is subjected comprises both hoop stresses, which subject the ring material to circumferential tension, and radial stresses, which subject the material to translaminar tension and shear. In the radial direction, the tensile stresses are carried by the matrix material only, which is relatively weak. Since the radial tensile stress depends upon the ring thickness-to-radius ratio, the ring must be relatively thin to maintain the stresses within the limits of the matrix material. Also, to achieve the required high energy storage densities, materials with a high strength to weight ratio are necessary.
The materials with the highest strength-to-weight ratios currently are fiber materials such as those used for the reinforcement of plastic composites. The fiber composites, therefore, offer the potential of very high energy storage densities. Problems, exist, however, due to orthotropic properties of the composites. They possess very high strength in the direction of the fibers, that is, in a circumferential direction, and very little transverse strength, that is, in a radial direction. Thus, fiber composite materials can withstand only very limited radial forces.
A theoretical ring with no radial thickness would not be subjected to any radial stress but to hoop stresses only. Thus, to limit the radial stresses in such rings to acceptable values, their radial thicknesses must be relatively small. Because the thickness of the rotor ring must necessarily be small in comparison to its diameter, means such as spokes must be provided for structurally connecting the ring to a central hub which is mounted on the motor-generator shaft.
Spokes for supporting high-speed rotor rings of flywheels must satisfy several basic mechanical requirements. They must provide a stable connection between the flywheel hub and ring. This connection must maintain the concentricity and geometric alignment needed for static and dynamic balance and must be rigid enough to resist the radial and gyroscopic forces which may be imposed. In addition, the spokes must transmit the torque required for high rates of ring acceleration and deceleration.
The spokes for fiber-reinforced composite rotors, such as employed for the storage of inertial energy, have special requirements due to the fact that such rotors have very little strength to resist the shear and flexure stresses which spokes would normally impose upon the rotor ring. The unidirectional fiber-reinforced composites are also very weak in transverse tension. Consequently, the spokes must not impose high radial forces upon the rotor ring at the point of attachment. Any radial loading imposed by the spokes will produce shear and flexure stresses throughout the rotor in addition to the local radial stresses at the attachment point. Such loads may also result in failure of the spoke-to-ring bond.
At high speed, the rotor ring dilates under the action of centrifugal force which produces a high circumferential tensile stress in the ring. The amount of dilation is equal to the product of the initial radius of the ring and the ratio of circumferential tensile stress to the modulus of elasticity of the rotor material. Continuity requires that the spokes must stretch to maintain contact with the rotor ring and the degree of extension must equal the dilation of the ring. The radial stretch of the spokes is equal to the inside radius of the rotor ring at the point of attachment times the ratio of the spoke stress to the spoke modulus of elasticity. Spokes directly attached to a rotor ring will generally require a high radial force to stretch the spoke enough to maintain contact with the ring.
Under the high centrifugal forces to which rotors of the type disclosed in the above referenced U.S. patents are subjected, and the resulting radial dilation, a fiber-reinforced composite spoke simply fastened to the ring produces an excessive radial force on the ring and the bond.
In addition, in order to adequately carry the torsional forces transmitted from the rotor hub to the ring under high rates of acceleration and deceleration, the spokes should be angled rather than radial. This results in the spokes being subjected to a transverse component of centrifugal force which creates bending moments in the spoke. At high rotational speeds these bending moments are significant both because of the high transverse forces and the increased effective stiffness of the spoke under centrifugal elongation.
Thus, it is apparent that prior art inertial energy storage rotors with spokes have serious drawbacks which limit their potential use and which correspondingly limit development of an otherwise highly desirable energy source.